How does one use cycle's image sequence?
You can use a sequence of numbered images as the input to an Image Texture node set to Image Sequence.
The key is to ensure your image filenames include a numeric element to represent the frame as the last part of the filename before the file extension - eg, 'flame_heat_fuel_000002.exr'.



Blender will identify the 'frame' part of the filename (in this case '000002') and use that to determine which image to pickup for the current animation frame, with the Frames, Start Frame, Offset manipulate how the Blender current frame maps to one of the image sequence frames :


'Frames' defines how many frames are in the sequence
'Start Frame' defines which timeline frame maps to the first image in the sequence
'Offset' shifts the animation along the image sequence by the specified number of frames (so an Offset of zero will map 1 to 1, 2 to 2, etc., while an offset of, say, 5 will map 1 to 6, 2 to 7, etc.)


Enable 'Cyclic' so as to loop the animation over the specified number of frames.

The Image Texture node shows the actual in-use frame just above the 'Frames' field. As you move along the timeline this will update to show which of the image frames is currently selected.